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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 388080.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.bm1 | 388080bm4 | \([0, 0, 0, -232784643, -1367018098558]\) | \(3971101377248209009/56495958750\) | \(19846919103133731840000\) | \([2]\) | \(56623104\) | \(3.4182\) | |
| 388080.bm2 | 388080bm2 | \([0, 0, 0, -14965923, -20070697822]\) | \(1055257664218129/115307784900\) | \(40507397865371127398400\) | \([2, 2]\) | \(28311552\) | \(3.0716\) | |
| 388080.bm3 | 388080bm1 | \([0, 0, 0, -3535203, 2221492322]\) | \(13908844989649/1980372240\) | \(695700869778968739840\) | \([2]\) | \(14155776\) | \(2.7250\) | \(\Gamma_0(N)\)-optimal |
| 388080.bm4 | 388080bm3 | \([0, 0, 0, 19961277, -99823466302]\) | \(2503876820718671/13702874328990\) | \(-4813792779255603805347840\) | \([2]\) | \(56623104\) | \(3.4182\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.bm do not have complex multiplication.Modular form 388080.2.a.bm
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
